scholarly journals A Constraint Programming Approach for Solving a Queueing Control Problem

2008 ◽  
Vol 32 ◽  
pp. 123-167 ◽  
Author(s):  
D. Terekhov ◽  
J. C. Beck
Keyword(s):  
Waiting Time ◽  
Constraint Programming ◽  
Programming Model ◽  
Programming Models ◽  
Programming Approach ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Problem Instances ◽  
Constraint Programming Model ◽  
Over Time

In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and several shaving procedures for these models are presented. Experimental results show that a model based on closed-form expressions together with a combination of shaving procedures is the most efficient. This model is able to find and prove optimal solutions for many problem instances within a reasonable run-time. Previously, the only available approach was a heuristic algorithm. Furthermore, a hybrid method combining the heuristic and the best constraint programming method is shown to perform as well as the heuristic in terms of solution quality over time, while achieving the same performance in terms of proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such queueing-based problems with constraint programming.

A multi-shop integrated scheduling algorithm with fixed output constraint

2021 ◽  
pp. 1-9
Author(s):  
Yingchun Xia ◽  
Zhiqiang Xie ◽  
Yu Xin ◽  
Xiaowei Zhang
Keyword(s):  
Constraint Programming ◽  
Programming Model ◽  
Scheduling Algorithm ◽  
Processing Parameters ◽  
Scheduling Problem ◽  
Integrated Scheduling ◽  
Scheduling Scheme ◽  
Wide Range ◽  
Constraint Programming Model ◽  
Output Constraint

The customized products such as electromechanical prototype products are a type of product with research and trial manufacturing characteristics. The BOM structures and processing parameters of the products vary greatly, making it difficult for a single shop to meet such a wide range of processing parameters. For the dynamic and fuzzy manufacturing characteristics of the products, not only the coordinated transport time of multiple shops but also the fact that the product has a designated output shop should be considered. In order to solve such Multi-shop Integrated Scheduling Problem with Fixed Output Constraint (MISP-FOC), a constraint programming model is developed to minimize the total tardiness, and then a Multi-shop Integrated Scheduling Algorithm (MISA) based on EGA (Enhanced Genetic Algorithm) and B&B (Branch and Bound) is proposed. MISA is a hybrid optimization method and consists of four parts. Firstly, to deal with the dynamic and fuzzy manufacturing characteristics, the dynamic production process is transformed into a series of time-continuous static scheduling problem according to the proposed dynamic rescheduling mechanism. Secondly, the pre-scheduling scheme is generated by the EGA at each event moment. Thirdly, the jobs in the pre-scheduling scheme are divided into three parts, namely, dispatched jobs, jobs to be dispatched, and jobs available for rescheduling, and at last, the B&B method is used to optimize the jobs available for rescheduling by utilizing the period when the dispatched jobs are in execution. Google OR-Tools is used to verify the proposed constraint programming model, and the experiment results show that the proposed algorithm is effective and feasible.

scholarly journals Solution of Quadratic Programming with Interval Variables Using a Two-Level Programming Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Syaripuddin ◽  
Herry Suprajitno ◽  
Fatmawati
Keyword(s):  
Quadratic Programming ◽  
Programming Model ◽  
Programming Models ◽  
Programming Approach ◽  
Optimum Point ◽  
Interval Variables ◽  
Interval Coefficients ◽  
Optimum Solution

Quadratic programming with interval variables is developed from quadratic programming with interval coefficients to obtain optimum solution in interval form, both the optimum point and optimum value. In this paper, a two-level programming approach is used to solve quadratic programming with interval variables. Procedure of two-level programming is transforming the quadratic programming model with interval variables into a pair of classical quadratic programming models, namely, the best optimum and worst optimum problems. The procedure to solve the best and worst optimum problems is also constructed to obtain optimum solution in interval form.

A solution method for treatment scheduling in rehabilitation hospitals with real-life requirements

2018 ◽  
Vol 30 (4) ◽  
pp. 367-386 ◽  
Author(s):  
Liyang Xiao ◽  
Mahjoub Dridi ◽  
Amir Hajjam El Hassani ◽  
Wanlong Lin ◽  
Hongying Fei
Keyword(s):  
Waiting Time ◽  
Programming Model ◽  
Search Algorithm ◽  
Real Life ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Mixed Integer ◽  
Solution Quality ◽  
Improved Cuckoo Search Algorithm ◽  
Rehabilitation Hospitals

Abstract In this study, we aim to minimize the total waiting time between successive treatments for inpatients in rehabilitation hospitals (departments) during a working day. Firstly, the daily treatment scheduling problem is formulated as a mixed-integer linear programming model, taking into consideration real-life requirements, and is solved by Gurobi, a commercial solver. Then, an improved cuckoo search algorithm is developed to obtain good quality solutions quickly for large-sized problems. Our methods are demonstrated with data collected from a medium-sized rehabilitation hospital in China. The numerical results indicate that the improved cuckoo search algorithm outperforms the real schedules applied in the targeted hospital with regard to the total waiting time of inpatients. Gurobi can construct schedules without waits for all the tested dataset though its efficiency is quite low. Three sets of numerical experiments are executed to compare the improved cuckoo search algorithm with Gurobi in terms of solution quality, effectiveness and capability to solve large instances.

scholarly journals A new constraint programming model and solving for the cyclic hoist scheduling problem

Constraints ◽  
2020 ◽  
Vol 25 (3-4) ◽  
pp. 319-337 ◽  
Author(s):  
Mark Wallace ◽  
Neil Yorke-Smith
Keyword(s):  
Constraint Programming ◽  
Programming Model ◽  
State Of The Art ◽  
Scale Up ◽  
Generic Model ◽  
Scheduling Problem ◽  
Hoist Scheduling ◽  
Wide Range ◽  
Constraint Programming Model ◽  
High Level

AbstractThe cyclic hoist scheduling problem (CHSP) is a well-studied optimisation problem due to its importance in industry. Despite the wide range of solving techniques applied to the CHSP and its variants, the models have remained complicated and inflexible, or have failed to scale up with larger problem instances. This article re-examines modelling of the CHSP and proposes a new simple, flexible constraint programming formulation. We compare current state-of-the-art solving technologies on this formulation, and show that modelling in a high-level constraint language, MiniZinc, leads to both a simple, generic model and to computational results that outperform the state of the art. We further demonstrate that combining integer programming and lazy clause generation, using the multiple cores of modern processors, has potential to improve over either solving approach alone.

A Stochastic Programming Approach for Locating and Dispatching Two Types of Ambulances

2021 ◽  
Vol 55 (2) ◽  
pp. 275-296
Author(s):  
Soovin Yoon ◽  
Laura A. Albert ◽  
Veronica M. White
Keyword(s):  
Stochastic Programming ◽  
Large Scale ◽  
Simulation Analysis ◽  
Programming Model ◽  
Prehospital Care ◽  
Programming Approach ◽  
Solution Technique ◽  
Solution Approach ◽  
Stochastic Solution ◽  
Problem Instances

Emergency Medical Service systems aim to respond to emergency calls in a timely manner and provide prehospital care to patients. This paper addresses the problem of locating multiple types of emergency vehicles to stations while taking into account that vehicles are dispatched to prioritized patients with different health needs. We propose a two-stage stochastic-programming model that determines how to locate two types of ambulances in the first stage and dispatch them to prioritized emergency patients in the second stage after call-arrival scenarios are disclosed. We demonstrate how the base model can be adapted to include nontransport vehicles. A model formulation generalizes the base model to consider probabilistic travel times and general utilities for dispatching ambulances to prioritized patients. We evaluate the benefit of the model using two case studies, a value of the stochastic solution approach, and a simulation analysis. The case study is extended to study how to locate vehicles in the model extension with nontransport vehicles. Stochastic-programming models are computationally challenging for large-scale problem instances, and, therefore, we propose a solution technique based on Benders cuts.

A constraint programming model with time uncertainty for cooperative flight departures

2018 ◽  
Vol 96 ◽  
pp. 170-191 ◽  
Author(s):  
Nina Schefers ◽  
Juan José Ramos González ◽  
Pau Folch ◽  
José Luis Munoz-Gamarra
Keyword(s):  
Constraint Programming ◽  
Programming Model ◽  
Time Uncertainty ◽  
Constraint Programming Model

Manufacturing cell formation with flexible processing capabilities and worker assignment: Comparison of constraint programming and integer programming approaches

2017 ◽  
Vol 232 (11) ◽  
pp. 2054-2068 ◽  
Author(s):  
Adil Baykasoğlu ◽  
Şeyda Topaloğlu ◽  
Filiz Şenyüzlüler
Keyword(s):  
Integer Programming ◽  
Constraint Programming ◽  
Manufacturing Systems ◽  
High Efficiency ◽  
Programming Model ◽  
Cell Formation ◽  
Programming Approach ◽  
Cell Formation Problem ◽  
Formation Problem ◽  
Complex Constraints

Cell formation deals with grouping of machines and parts in manufacturing systems according to their compatibility. Manufacturing processes are surrounded with an abundance of complex constraints which should be considered carefully and represented clearly for obtaining high efficiency and productivity. Constraint programming is a new approach to combinatorial optimization and provides a rich language to represent complex constraints easily. However, the cell formation problems are well suited to be solved by constraint programming approach since the problem has many constraints such as part-machine requirements, availabilities in the system in terms of capacity, machine and worker abilities. In this study, the cell formation problem is modeled using machine, part processing and worker flexibilities via resource element–based representation. Resource elements define the processing requirements of parts and processing capabilities of machines and workers, which are resource-independent capability units. A total of 12 case problems are generated, and different search phases of constraint programming are defined for the solution procedure. The cell formation problem is modeled in both constraint programming and integer programming, and a comparative analysis of constraint programming and integer programming model solutions is done. The results indicate that both the models are effective and efficient in the solution of the cell formation problem.

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